If a teacher instructs with greater attention to improving students' performance in order to protect her employment rather than solely to advance knowledge or character, is she acting immorally? This question has historical roots in Socrates's famed animosity toward the sophists. Socrates maintained that sophistic teaching was immoral because the teacher's self-interest was at the center of the relationship rather than fostering "arete". Socrates differentiated his work from teaching per se. Nevertheless, both Socrates and the sophists are examples of the historically precarious position of educators. In the classic Greek story, these pedagogues were at the mercy of sociopolitical forces outside of their control and the societal view of their work was subject to the vicissitudes of Athenian state interests, ideology, and politics. Those charged with fostering children's cultural, social, and intellectual literacy, as Socrates and the sophists were, often find themselves in the middle of conflicting social and economic factors. In the question of what it means for educators to act morally in this milieu, classical liberalism and ethics premised on impartial, objective, and decontextualized ideal theory have been the primary lens. As a consequence, it is an open question whether these frameworks can take into account the multifarious directions in which society pulls educators today. This paper addresses one prevailing rendering of the moral basis of teaching. In the Moral Work of Teaching (MWT) framework, Osguthorpe and Sanger draw upon the liberal democratic ethic, virtue ethics, and psychological theories to argue for the inherent morality of teaching in K-12 settings. On their view, such an inquiry can fall into the dichotomous categories of "teaching morally" and "teaching morality". While the two domains are related, it is the former that proposes grounds for viewing teaching as a moral act. Based on one co-author's experiences, this paper discusses an iteration of the New York City small schools movement reform over the last decade as a clear example of the constraints that accountability policies exert on "teaching morally"; indeed these limiting factors are so pervasive as to warrant rethinking what it means to be a moral teacher.